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Question
Priyanka has a recurring deposit account of Rs. 1000 per month at 10% per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held.
Solution
Amount of recurring deposit per month = Rs. 1000
Rate of interest = 10 % p.a
let period = n months
Amount of interest = 5550 .....(1)
Total principal for one month = `(1000xxn(n+1))/2`
`"Interest" = (1000n(n+1))/2 xx 10/100 xx 1/12`
`= 25/6 n (n+1)` ......(2)
From (1) nd (2) , we get
`25/6n(n+1) = 5550`
`25n^2 + 25n = 33300`
`25n^2 + 25n - 33300 = 0`
`n^2 + n - 1332 = 0`
`n^2 + 37n - 36n - 1332 = 0`
`n(n+37) - 36(n+37) = 0`
(n - 36)(n + 37) = 0
n = 36
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